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Mathematics in a Mathematics in a Liberal Arts Liberal Arts

ProgramProgram

Riaz SaloojeeRiaz SaloojeeSeneca CollegeSeneca College

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OverviewOverview

My backgroundMy background GAS programGAS program Math within GASMath within GAS Reconceptualizing math within GASReconceptualizing math within GAS Overview of coursesOverview of courses Successes/shortcomingsSuccesses/shortcomings Example of a unit (graph theory)Example of a unit (graph theory)

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My BackgroundMy Background

My previous graduate work was in My previous graduate work was in mathematicsmathematics

Current PhD is in math educationCurrent PhD is in math education– Transition from secondary to college Transition from secondary to college

mathmath Taught elementary (grade 5)*Taught elementary (grade 5)* And secondaryAnd secondary Teaching math in GAS for last 5 yearsTeaching math in GAS for last 5 years

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GAS ProgramGAS Program

General Arts & Science (GAS) is General Arts & Science (GAS) is predominantly an arts articulation predominantly an arts articulation programprogram

Large increase in intake in past 5 Large increase in intake in past 5 years (currently about 1000 years (currently about 1000 students)students)

Strong focus on humanities and Strong focus on humanities and liberal artsliberal arts

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Math in GASMath in GAS

Students required to complete a Students required to complete a math course in their first semestermath course in their first semester

Placed in one of 3 math courses Placed in one of 3 math courses based on CPT results and math based on CPT results and math backgroundbackground

Math is (essentially) a breadth Math is (essentially) a breadth requirementrequirement

Terminal math course for 80-90% Terminal math course for 80-90% of studentsof students

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Reconceptualizing Reconceptualizing Math within GASMath within GAS 5 years ago – courses offered: 5 years ago – courses offered:

fundamentals of math, basic fundamentals of math, basic algebra, algebra, intermediate algebraintermediate algebra, , calculuscalculus

Curriculum was a regurgitation of Curriculum was a regurgitation of topics covered in high school topics covered in high school (more of the same)(more of the same)

Students were disinterested and Students were disinterested and viewed math as an obstacle/hoopviewed math as an obstacle/hoop

High level of math phobiaHigh level of math phobia

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Began to ask:Began to ask:– Why are students required to take Why are students required to take

math?math?– Why this particular math content?Why this particular math content?– What is it we really want students to get What is it we really want students to get

from a one-semester, terminal course?from a one-semester, terminal course? Some answers: to foster a Some answers: to foster a

“mathematical way of knowing”; “mathematical way of knowing”; gain an appreciation of its cultural gain an appreciation of its cultural importance; (mostly) to engage in importance; (mostly) to engage in ((toto dodo) some mathematics of interest ) some mathematics of interest to students (to have that to students (to have that mathematical aesthetic experience)mathematical aesthetic experience)

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Hence, our point of departure Hence, our point of departure from the traditional curriculum from the traditional curriculum (luckily we had the support of a (luckily we had the support of a trusting (trusting (too trusting?too trusting?) chair)) chair)

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Overview of New Math Overview of New Math CurriculaCurricula New courses are a “survey” of New courses are a “survey” of

some topics in discrete math, some topics in discrete math, combinatorics and number theorycombinatorics and number theory

Content areas:Content areas:– Graph (network) theoryGraph (network) theory– Voting methodsVoting methods– Number theory (intro to coding theory)Number theory (intro to coding theory)– ProbabilityProbability– Game theoryGame theory

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Approach:Approach:– to engage students in meaningful to engage students in meaningful

mathematics through discovery, mathematics through discovery, problem solving, and discussionsproblem solving, and discussions

– Problem-centredProblem-centred– Small group workSmall group work– Strong emphasis on exploration, Strong emphasis on exploration,

discussion and explanationsdiscussion and explanations– Greater focus on conceptual Greater focus on conceptual

understanding than procedural understanding than procedural competencycompetency

These topic areas lend These topic areas lend themselves nicely to this themselves nicely to this approachapproach

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Successes/Successes/ShortcomingsShortcomings Much higher level of student Much higher level of student

engagement and interestengagement and interest Levels the playing field Levels the playing field

(mathematical backgrounds)(mathematical backgrounds) Importance of subject clearly Importance of subject clearly

evident (topics always related to evident (topics always related to current work and contemporary current work and contemporary applications)applications)

My increased enjoyment teaching My increased enjoyment teaching this contentthis content

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Students have a rich experience Students have a rich experience and increased self-efficacy with and increased self-efficacy with mathematicsmathematics– ““I never thought math could be I never thought math could be

interesting or that I could be good at interesting or that I could be good at it.” (these are related)it.” (these are related)

Shortcoming:Shortcoming:– Although focus is on “thinking Although focus is on “thinking

mathematically” courses don’t mathematically” courses don’t necessarily provide content that necessarily provide content that students may need were they to students may need were they to transfer to technology-oriented transfer to technology-oriented programs programs

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An example unit…An example unit…

GraphGraph

TheoryTheory